How do you determine the vertex of this equation f(x)= - 1/2x^2-x+3/2. By completing the square? THanks.

Question

anonymous · Answer

yes. Completing the square will put the equation into vertex form
$$y = m(x-p)^2 + q$$
the vertex will then be (p,q).

anonymous · Answer

How do you complete the squre should of have been the question.

anonymous · Answer

$$ y=-\frac{1}{2}x^2-x + \frac{3}{2}$$ becomes 
$$-2y=x^2 +2x -3$$
becomes
$$-2y = x^2 +2x +1^2 -1^2 -3$$

$$-2y = \left[x^2 +2x +1^2\right] -1^2 -3$$ becomes


$$-2y = \left[(x+1)^2\right] -4$$ becomes

$$y = -\frac{1}{2}(x+1)^2 +2$$ 
p=-1, q=2 vertex =(-1,2)

anonymous · Answer

Thank you very much!